After 10 years of marriage, Ashley and Charles have decided to separate. Charles will take the custody of the children and will stay home for the next 8 years. Since Charles will have no income, Ashley will pay him to help support him and the children until he returns to work after 8 years. The problem at hand is to determine whether a lump sum or a periodic annuity is better for both of them.

Assume that periodic payments are taxable for the recipient and tax deductible for the payer, while lump sum payments are not taxable for the recipient and not tax deductible for the payer.

Assume that the lump sum will be paid one year from today and if the payment is periodic then the first annual payment will be today. Charles has a marginal tax rate of 21% while Ashley has a marginal tax rate of 46%. Suppose they can earn a before tax nominal rate of return of 6% per year.

a. What are their after taxes rates of return?

b. Ashley offers a lump sum of $150,000. What before tax annual payment stream for 8 years is equivalent to the lump sum from her point of view?

c. Charles asks for a lump sum of $170,000. What before tax annual payment stream for 8 years is equivalent to the lump sum for him?

d. Based on your answer to b) and c) is there a way that they both could be better off. If yes, then what should be the amount of payment or payments?

e. Suppose they both agreed on a before tax annual payment of $35,000 today. Payments will decline at 3% per year in real terms. In total there will be 8 payments. If the inflation rate is 2% then what is expected present value of after tax payments from Ashley? and after tax receipt to Charles?